Temperature-dependence of charge and exciton transport in one-dimensional systems subject to static and dynamic disorder

The temperature dependence of dynamical properties (e.g., the asymptotic diffusion coefficient and the subdiffusive exponent) is calculated for charges and excitons in one-dimensional systems subject to static and dynamic disorder. These properties are determined by three complementary methods. One approach is based on the time integration of the velocity autocorrelation function. The second approach is based on the mean-squared displacement of thermal wave packets subject to stochastic collapse via Lindblad jump operators. These two methods are applicable in the high-temperature regime, where the noise is temporally uncorrelated. In this regime, the noise causes particle localization, and the transport is diffusive. The third approach-applicable in the low-temperature regime-is weak-coupling Redfield theory. Here, static disorder causes Anderson localization. When the dynamics is diffusive, the diffusion coefficient is a nonmonotonic function of temperature, increasing with temperature in the low-temperature Environment-Assisted Quantum Transport (ENAQT) regime and decreasing with temperature in the high-temperature Quantum-Zeno (QZ) regime. For any temperature, static disorder decreases the diffusion coefficient. Increasing the dephasing factor increases the diffusion coefficient in the ENAQT regime, whereas the diffusion coefficient decreases in the QZ regime. The dynamics is nondiffusive for thermal energies deep within the manifold of local ground states, where the subdiffusive exponent decreases with increasing disorder and decreasing temperature.